Algebraic Foundations of Many-Valued Reasoning
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Kluwer Academic Publishers (1999)
This unique textbook states and proves all the major theorems of many-valued propositional logic and provides the reader with the most recent developments and trends, including applications to adaptive error-correcting binary search. The book is suitable for self-study, making the basic tools of many-valued logic accessible to students and scientists with a basic mathematical knowledge who are interested in the mathematical treatment of uncertain information. Stressing the interplay between algebra and logic, the book contains material never before published, such as a simple proof of the completeness theorem and of the equivalence between Chang's MV algebras and Abelian lattice-ordered groups with unit - a necessary prerequisite for the incorporation of a genuine addition operation into fuzzy logic. Readers interested in fuzzy control are provided with a rich deductive system in which one can define fuzzy partitions, just as Boolean partitions can be defined and computed in classical logic. Detailed bibliographic remarks at the end of each chapter and an extensive bibliography lead the reader on to further specialised topics.
|Keywords||Many-valued logic Proposition (Logic|
|Categories||categorize this paper)|
|Buy the book||$92.49 used (56% off) $151.73 new (28% off) $152.92 direct from Amazon (27% off) Amazon page|
|Call number||QA9.45.C54 1999|
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Citations of this work BETA
Hector Freytes (2010). Quantum Computational Structures: Categorical Equivalence for Square Root qMV -Algebras. Studia Logica 95 (1/2):63 - 80.
Petr Hájek (2010). Some (Non)Tautologies of Łukasiewicz and Product Logic. Review of Symbolic Logic 3 (2):273-278.
M. L. Dalla Chiara, A. Ledda, G. Sergioli & R. Giuntini (2013). The Toffoli-Hadamard Gate System: An Algebraic Approach. [REVIEW] Journal of Philosophical Logic 42 (3):467-481.
Anatolij Dvurečenskij & Yongjian Xie (2012). Atomic Effect Algebras with the Riesz Decomposition Property. Foundations of Physics 42 (8):1078-1093.
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